Lining and Surrounding Rock in Non-circular Tunnel Based on Complex Variable Method

A complex variable method is presented of stress and displacement problems for a non-circular deep tunnel with a certain given boundary conditions at infinity. Firstly, in order to overcome the complex problems caused by non-circular geometric configurations and the lining supports, optimal design method are used to determine coefficients of the conformal mapping function. Secondly, The problem of the multiply connected region is overcome by Power series complex function method, which determine stress and displacement within tunnel lining and within surrounding rock. The coefficients in the stress functions are determined by complex variable method. Finally, the complex variable method is validated by FLAC finite difference software through an example. Both the complex variable method and the numerical simulation obtain the similar results of the stress concentration and the minimum radial displacement occurs at a similar place of tunnel. It is demonstrated that the complex variable complex variable method is reliable and reasonable. Under deep buried conditions, the complex variable method does not need to establish models and mesh according to different burial depth and working conditions. Only mapping function and boundary conditions are required for the calculation. The complex variable method overcomes the problems of inaccuracy and slow calculation caused by meshing dimension and other problems in software calculation. And it also provides another way for solving non-circular tunnel excavation problems in the range of elasticity in a fast and accurate way.